Lecture: The Truth About Linear Regression (Advanced Data Analysis from an Elementary Point of View)

Lecture 2, The truth about linear regression: Using Taylor's theorem to
justify linear regression locally. Collinearity. Consistency of ordinary
least squares estimates under weak conditions (non-Gaussian noise,
non-independent noise, non-constant variance, dependent predictors). Linear
regression coefficients will change with the distribution of the input
variables: examples. Why \( R^2 \) is usually a distraction. Linear
regression coefficients will change with the distribution of unobserved
variables (omitted variable effects). Errors in variables. Transformations of
inputs and of outputs. Utility of probabilistic assumptions; the importance of
looking at the residuals. What it really means when coefficients are
significantly non-zero. What "controlled for in a linear regression" really
means.